Why do cats stare out the window?

Right now, my big cat is sitting on my
computer desk and staring off into the
distance out the window.
What's he looking at?
I can't see anything, but he seems very
upset by something outside the window.
His eyes are small and his mouth is very tight
as if he's scared.
Maybe he's just contemplating the sky!
Have you ever seen your cat stare out the window
at some imaginary thing? What are cats looking at
when they stare out the window?
Is there something out there, I can't see?